Stacks And Categories In Geometry Topology And Algebra

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Stacks and Categories in Geometry, Topology, and Algebra

Author : Tony Pantev
Publisher :
ISBN 13 : 9781470425685
Total Pages : 323 pages
Book Rating : 4.4/5 (256 download)

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Book Synopsis Stacks and Categories in Geometry, Topology, and Algebra by : Tony Pantev

Download or read book Stacks and Categories in Geometry, Topology, and Algebra written by Tony Pantev and published by . This book was released on 2015 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the CATS4 Conference on Higher Categorical Structures and their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, held from July 2-7, 2012, at CIRM in Luminy, France. Over the past several years, the CATS conference series has brought together top level researchers from around the world interested in relative and higher category theory and its applications to classical mathematical domains. Included in this volume is a collection of articles covering the applications of categories and stacks to geometry, topology and algebra. Techniques such as localization, model categories, simplicial objects, sheaves of categories, mapping stacks, dg structures, hereditary categories, and derived stacks, are applied to give new insight on cluster algebra, Lagrangians, trace theories, loop spaces, structured surfaces, stability, ind-coherent complexes and 1-affineness showing up in geometric Langlands, branching out to many related topics along the way

Stacks and Categories in Geometry, Topology, and Algebra

Author : Tony Pantev
Publisher : American Mathematical Soc.
ISBN 13 : 1470415577
Total Pages : 334 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Stacks and Categories in Geometry, Topology, and Algebra by : Tony Pantev

Download or read book Stacks and Categories in Geometry, Topology, and Algebra written by Tony Pantev and published by American Mathematical Soc.. This book was released on 2015-06-26 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the CATS4 Conference on Higher Categorical Structures and their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, held from July 2-7, 2012, at CIRM in Luminy, France. Over the past several years, the CATS conference series has brought together top level researchers from around the world interested in relative and higher category theory and its applications to classical mathematical domains. Included in this volume is a collection of articles covering the applications of categories and stacks to geometry, topology and algebra. Techniques such as localization, model categories, simplicial objects, sheaves of categories, mapping stacks, dg structures, hereditary categories, and derived stacks, are applied to give new insight on cluster algebra, Lagrangians, trace theories, loop spaces, structured surfaces, stability, ind-coherent complexes and 1-affineness showing up in geometric Langlands, branching out to many related topics along the way.

Algebraic Spaces and Stacks

Author : Martin Olsson
Publisher : American Mathematical Soc.
ISBN 13 : 1470427982
Total Pages : 313 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Algebraic Spaces and Stacks by : Martin Olsson

Download or read book Algebraic Spaces and Stacks written by Martin Olsson and published by American Mathematical Soc.. This book was released on 2016-05-13 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix.

Algebraic Spaces and Stacks

Author : Martin Olsson
Publisher : American Mathematical Society
ISBN 13 : 1470474808
Total Pages : 313 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Algebraic Spaces and Stacks by : Martin Olsson

Download or read book Algebraic Spaces and Stacks written by Martin Olsson and published by American Mathematical Society. This book was released on 2023-09-15 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix. It is splendid to have a self-contained treatment of stacks, written by a leading practitioner. Finally we have a reference where one can find careful statements and proofs of many of the foundational facts in this important subject. Researchers and students at all levels will be grateful to Olsson for writing this book. —William Fulton, University of Michigan This is a carefully planned out book starting with foundations and ending with detailed proofs of key results in the theory of algebraic stacks. —Johan de Jong, Columbia University

Derived $\ell $-Adic Categories for Algebraic Stacks

$Download Derived $\ell $-Adic Categories for Algebraic Stacks PDF Online Free$

Author : Kai Behrend
Publisher : American Mathematical Soc.
ISBN 13 : 0821829297
Total Pages : 110 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Derived $\ell $-Adic Categories for Algebraic Stacks by : Kai Behrend

Download or read book Derived $\ell $-Adic Categories for Algebraic Stacks written by Kai Behrend and published by American Mathematical Soc.. This book was released on 2003 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is intended for graduate students and research mathematicians interested in algebraic geometry, category theory and homological algebra.

Homotopical Algebraic Geometry II: Geometric Stacks and Applications

Author : Bertrand Toën
Publisher : American Mathematical Soc.
ISBN 13 : 0821840991
Total Pages : 242 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Homotopical Algebraic Geometry II: Geometric Stacks and Applications by : Bertrand Toën

Download or read book Homotopical Algebraic Geometry II: Geometric Stacks and Applications written by Bertrand Toën and published by American Mathematical Soc.. This book was released on 2008 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second part of a series of papers called "HAG", devoted to developing the foundations of homotopical algebraic geometry. The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category, such as derivations, étale and smooth morphisms, flat and projective modules, etc. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category $C$, and prove that this notion satisfies the expected properties.

Simplicial Methods for Operads and Algebraic Geometry

Author : Ieke Moerdijk
Publisher : Springer Science & Business Media
ISBN 13 : 3034800525
Total Pages : 186 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Simplicial Methods for Operads and Algebraic Geometry by : Ieke Moerdijk

Download or read book Simplicial Methods for Operads and Algebraic Geometry written by Ieke Moerdijk and published by Springer Science & Business Media. This book was released on 2010-12-01 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. It is based on lectures delivered at the Centre de Recerca Matemàtica in February 2008, as part of a special year on Homotopy Theory and Higher Categories"--Foreword

Introduction to Algebraic Geometry and Algebraic Groups

Author :
Publisher : Elsevier
ISBN 13 : 008087150X
Total Pages : 373 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Introduction to Algebraic Geometry and Algebraic Groups by :

Download or read book Introduction to Algebraic Geometry and Algebraic Groups written by and published by Elsevier. This book was released on 1980-01-01 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Algebraic Geometry and Algebraic Groups

Stacks Project Expository Collection

Author : Pieter Belmans
Publisher : Cambridge University Press
ISBN 13 : 1009063286
Total Pages : 308 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Stacks Project Expository Collection by : Pieter Belmans

Download or read book Stacks Project Expository Collection written by Pieter Belmans and published by Cambridge University Press. This book was released on 2022-09-30 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Stacks Project Expository Collection (SPEC) compiles expository articles in advanced algebraic geometry, intended to bring graduate students and researchers up to speed on recent developments in the geometry of algebraic spaces and algebraic stacks. The articles in the text make explicit in modern language many results, proofs, and examples that were previously only implicit, incomplete, or expressed in classical terms in the literature. Where applicable this is done by explicitly referring to the Stacks project for preliminary results. Topics include the construction and properties of important moduli problems in algebraic geometry (such as the Deligne–Mumford compactification of the moduli of curves, the Picard functor, or moduli of semistable vector bundles and sheaves), and arithmetic questions for fields and algebraic spaces.

Homotopical Algebraic Geometry II

Author : Bertrand Toën
Publisher :
ISBN 13 : 9781470405083
Total Pages : 242 pages
Book Rating : 4.4/5 (5 download)

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Book Synopsis Homotopical Algebraic Geometry II by : Bertrand Toën

Download or read book Homotopical Algebraic Geometry II written by Bertrand Toën and published by . This book was released on 2014-09-11 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category.

Fundamental Algebraic Geometry

Author : Barbara Fantechi
Publisher : American Mathematical Soc.
ISBN 13 : 0821842455
Total Pages : 354 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Fundamental Algebraic Geometry by : Barbara Fantechi

Download or read book Fundamental Algebraic Geometry written by Barbara Fantechi and published by American Mathematical Soc.. This book was released on 2005 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.

Categories and Sheaves

Author : Masaki Kashiwara
Publisher : Springer Science & Business Media
ISBN 13 : 3540279504
Total Pages : 496 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Categories and Sheaves by : Masaki Kashiwara

Download or read book Categories and Sheaves written by Masaki Kashiwara and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.

Affine Flag Manifolds and Principal Bundles

Author : Alexander Schmitt
Publisher : Springer Science & Business Media
ISBN 13 : 303460288X
Total Pages : 298 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Affine Flag Manifolds and Principal Bundles by : Alexander Schmitt

Download or read book Affine Flag Manifolds and Principal Bundles written by Alexander Schmitt and published by Springer Science & Business Media. This book was released on 2011-01-28 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Affine flag manifolds are infinite dimensional versions of familiar objects such as Graßmann varieties. The book features lecture notes, survey articles, and research notes - based on workshops held in Berlin, Essen, and Madrid - explaining the significance of these and related objects (such as double affine Hecke algebras and affine Springer fibers) in representation theory (e.g., the theory of symmetric polynomials), arithmetic geometry (e.g., the fundamental lemma in the Langlands program), and algebraic geometry (e.g., affine flag manifolds as parameter spaces for principal bundles). Novel aspects of the theory of principal bundles on algebraic varieties are also studied in the book.

Algebraic Geometry over C∞-Rings

Author : Dominic Joyce
Publisher : American Mathematical Soc.
ISBN 13 : 1470436450
Total Pages : 139 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Algebraic Geometry over C∞-Rings by : Dominic Joyce

Download or read book Algebraic Geometry over C∞-Rings written by Dominic Joyce and published by American Mathematical Soc.. This book was released on 2019-09-05 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: If X is a manifold then the R-algebra C∞(X) of smooth functions c:X→R is a C∞-ring. That is, for each smooth function f:Rn→R there is an n-fold operation Φf:C∞(X)n→C∞(X) acting by Φf:(c1,…,cn)↦f(c1,…,cn), and these operations Φf satisfy many natural identities. Thus, C∞(X) actually has a far richer structure than the obvious R-algebra structure. The author explains the foundations of a version of algebraic geometry in which rings or algebras are replaced by C∞-rings. As schemes are the basic objects in algebraic geometry, the new basic objects are C∞-schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps. The author also studies quasicoherent sheaves on C∞-schemes, and C∞-stacks, in particular Deligne-Mumford C∞-stacks, a 2-category of geometric objects generalizing orbifolds. Many of these ideas are not new: C∞-rings and C∞ -schemes have long been part of synthetic differential geometry. But the author develops them in new directions. In earlier publications, the author used these tools to define d-manifolds and d-orbifolds, “derived” versions of manifolds and orbifolds related to Spivak's “derived manifolds”.

Motivic Homotopy Theory

Author : Bjorn Ian Dundas
Publisher : Springer Science & Business Media
ISBN 13 : 3540458972
Total Pages : 228 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Motivic Homotopy Theory by : Bjorn Ian Dundas

Download or read book Motivic Homotopy Theory written by Bjorn Ian Dundas and published by Springer Science & Business Media. This book was released on 2007-07-11 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.

Grothendieck-Serre Correspondence

Author : Pierre Colmez
Publisher : American Mathematical Society, Société Mathématique de France
ISBN 13 : 1470469391
Total Pages : 600 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Grothendieck-Serre Correspondence by : Pierre Colmez

Download or read book Grothendieck-Serre Correspondence written by Pierre Colmez and published by American Mathematical Society, Société Mathématique de France. This book was released on 2022-05-25 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a bilingual (French and English) edition of the mathematical correspondence between A. Grothendieck and J-P. Serre. The original French text of 84 letters is supplemented here by the English translation, with French text printed on the left-hand pages and the corresponding English text printed on the right-hand pages. The book also includes several facsimiles of original letters. The letters presented in the book were mainly written between 1955 and 1965. During this period, algebraic geometry went through a remarkable transformation, and Grothendieck and Serre were among central figures in this process. The reader can follow the creation of some of the most important notions of modern mathematics, like sheaf cohomology, schemes, Riemann-Roch type theorems, algebraic fundamental group, motives. The letters also reflect the mathematical and political atmosphere of this period (Bourbaki, Paris, Harvard, Princeton, war in Algeria, etc.). Also included are a few letters written between 1984 and 1987. The letters are supplemented by J-P. Serre's notes, which give explanations, corrections, and references further results. The book should be useful to specialists in algebraic geometry, in history of mathematics, and to all mathematicians who want to understand how great mathematics is created.

Algebraic Topology and Related Topics

Author : Mahender Singh
Publisher : Springer
ISBN 13 : 9811357420
Total Pages : 313 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Algebraic Topology and Related Topics by : Mahender Singh

Download or read book Algebraic Topology and Related Topics written by Mahender Singh and published by Springer. This book was released on 2019-02-02 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the latest advances in algebraic topology, from homotopy theory, braid groups, configuration spaces and toric topology, to transformation groups and the adjoining area of knot theory. It consists of well-written original research papers and survey articles by subject experts, most of which were presented at the “7th East Asian Conference on Algebraic Topology” held at the Indian Institute of Science Education and Research (IISER), Mohali, Punjab, India, from December 1 to 6, 2017. Algebraic topology is a broad area of mathematics that has seen enormous developments over the past decade, and as such this book is a valuable resource for graduate students and researchers working in the field.